precalculus

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To what interval I must we restrict the parameter t if the graph of the parametric equations

x=t+1
y = 2t^2 +1

for t in the set I

is identical to the graph of the parametric equations

x = 1+ sin s
y = 2- cos(2s)

for s in [0,pi)?

  • precalculus -

    it appears we need
    1+t = 1+sin s,so
    t = sin s
    t must be in [0,1] if s is in [0,pi)

    also,
    2t^2+1 = 2-cos(2s)
    2t^2+1 = 2 - (1-2sin^2 s)
    2t^2+1 = 2sin^2 s + 1
    same domain.

  • precalculus -

    Thx!

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